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THS.

THE PRODUCTION AND VELOCITY
MEASUREMENTS OF
ULTRASONICS IN SEVERAL LIQUIDS

Thesis for the Degree of M. S.
MICHIGAN STATE COLLEGE

Grant 5. Bennett
194I

 

 

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01771 1916

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THE PRODUCTION AND VELOCITY MEASURExms
OF ULTRASONICS IN SEVERAL LIQUIDS

by
Grant S. Bennett

A.THESIS
Submitted to the Graduate School of Michigan
State College of Agriculture and Applied
Science in partial fulfilment of the
requirements for the degree or

MASTER OF SCIENCE

Department of Physics
1941

The author would like to take this opportunity to re-
commend that anyone interested in the field cf ultrasonics
read‘gltrasonics Eggighgig_8cientific'ggd Technical Applications
by Ludwig Bergmann. This book is a veritable gold mine of in-
formation to the research worker and shortcomings in theoretical
developments are well made up for in the same five hundred and
seventy-five references given in the bibliography. The author
has made constant reference to this book ti and instead of
attempting to give credit in each place suggests here that if
no other work be mentioned, Bergmann was consulted.

The author extends his sincere appreciation to Dr. J. W.
mcGrath who first aroused his interest in ultrasonics and.who
has guided this work. To list the others who have made sugges-
tions, loaned apparatus and given encouragement would be simply
to list the personnel of the department, and to all the author
is grateful. A special word of thanks should be addressed to
£rof._c. Wthhapman for his cooperation in the obtaining of

apparatus and supplies.

 

134210

TABLE OF CONTENTS

Page
Introduction _ 1
Theory 2
Apparatus 5
Experimental Procedure 10
Data 15
Discussion of Results 19
Conclusion and General Discussion 21

Literature Cited 23

-The Production and Velocity.Measurements of
Ultrasonics in Several Liquids

INTRODUCTION

Ultrasonic waves are, of course, sound waves of a fre-
quency above the audible range. ‘They are compressional waves,
with frequencies ranging from.20,000 key/sec -just above the
audible limit- up into the order of 10,000,000 key/sec. In
air (v-SSl m/sec) the wave-lengths then vary from the order
of 1 cm to 10‘4 cm” Thus the shorter ultrasonic waves are of
the same order of magnitude as light waves. There is a rather
great concentration of energy in these waves; Bergmann (1)
shows that for an intensity of 10 watts/cmz the sound radia-
tion pressure is 0.087 gr/emz. Intensities of this order are
not at all unusual, as contrasted with audible sound in which
intensities are on the order of 10’10 watts/cmZ.

By virtue of the short length of these waves, measure-
ments which require awkward and unwieldy apparatus for audible
sound can be carried forth in a much smaller Space, as a
number of wave-lengths can be produced where only a fraction
of an audible wave could be present. Likewise with the short
waves the influence of boundary walls is more easily removed.
Laws valid for the audible range hold true for the ultrasonic
range, although in the latter case phenomena appear which had
not been observed in the former.

It is the purpose of this investigation to construct
apparatus forthe production of ultrasonic waves, and to make

use of this apparatus to measure the velocity of sound in

various liquids. The variation of sound velocity with temp
perature is of particular interest. It will be shown that
the adiabatic compressibility and the ration of the specific
heats of a liquid can then be calculated, which are otherwise

rather difficult to measure and to compute.
saga:

Richards (2) gives for a plane wave travelling in a

-0 +l)

homogeneous isotropic medium the equation

a. ,, D
fl?! 3’10?
y/ ‘3:

(l) ;>.t ‘chs. /05
in.whichjfrepresents the displacement, x is the direction of
propagation of the wave, Pb and/ears the pressure and density
in the undisplaced portion of the substance, andI/is the ratio
of the specific heats. This equation is developed on the as-
sumption that the sound wave is transmitted adaibatically.

For very small amplitudes this equation gives the familiar re-
sult for the phase velocity

' DP
1?, -
(2) V01 5 «F; ’ (37.).J.
2P 1

in which -5” is evaluated.for the case - o
The compressibility/Q is defined as

' fo"

(3) P: -V "(f

From.this relation,it can be shown that the velocity of an

elastic wave is also given by

__ l
(4) 1r ; % - [FF/:1
in whichfi', is the isothermal compressibility andfigthe
adiabatic compressibility. ’

It is this last relation which gives to sound velocity
measurements one of their chief uses, for the adiabatic come
pressibility together with the isothermal compressibility
allows us to calculate directly the ratio of the specific heats.
From.this, we can calculate the specific heat at constant vol-
ume, which otherwise involves complicated thermodynamical re-
lations.

In 1952 Debye and Sears (3) and also Lucas and Biquard
showed independently of one another that light passing throught
a liquid traversed by a sound wave is diffracted and phenomena
appear very similar to those obtained with an ordinary trans-
mission grating. There are apparently two effects; the perio-
dically changing index of refraction bends the waves, and also
there is a periodic retardation of the light in various parts
of the sound beam. The effective grating space is the dis-
tance between successive compressions, or the wave-length of
the soundjl.It is shown that the ordinary grating law holds,

01'
‘5’ MA ’A/u'me

where n is the order of the diffraction image, 91s the angle
of diffraction for the nth order, and Ais the wave-length of

the light. Eq (5) combined with the eXpression for the
velocity of a wave velLVgives for the velocity of sound

(6) 4r; LES—1’
M6

Obviously the deviation of the orders depends upon the
frequency of the sound, higher frequencies causing greater
deviation. For example, in liquids the velocity is on the
order of 1200 m/sec, and for a frequency of 1800 key. the
deviation is on the order of 1.5 mm. at a distance of 200 cm.
This consideration shows that impossibility of using audible
sound in this manner, for a frequency of 20 key. would give
a deviation of about 0.0016 mm, and lower frequencies even
less.

This method gives us an easy way to measure the velocity
of sound, for the diffraction pattern may be preserved on a
photographic plate and the deviation of the orders measured
with considerable accuracy on a comparator. The other
measurements required are the distance of the plate from.the
lens, the frequency of the sound (the frequency of the driving
oscillator) and the wave-length of the light, all of which
can be made to a fairly high degree of accuracy.

Either standing or travelling sound waves may be used
in this method, the diffraction effects being affected only
slightly. In the case of travelling waves the grating is
moving across the light beam with the velocity of sound;
in the case of standing waves the grating is oscillating back
and forth across the light beam through a distancedgf.

 

W

There are several methods of producing ultrasonic waves,
of which probably the most convenient for the.maJority of
purposes is the piezo-electric effect of quartz crystals. It
is well known that if a difference of potential be applied to
opposite faces of a slab of quartz the slab will either expand
or contract in the direction normal to those faces, depending
upon the sign of the charge. If this differencel'of potential
be alternating the slab will vibrate, the vibrations being
maximum when the impressed frequency is equal to the natural
mechanical frequency of the quartz. The faces of the slab
thus give off sound waves, the frequency being determined by
the thickness of the slab.

The acaEtic crystal used in this investigation was an
ordinary one, produced for the control of oscillator circuits.
An I—cut crystal, was used as this type is thick enough to be
fairly rugged. The dimensions were 2.5 x 2.5 £7.11 cm.. The
temperature coefficient was given as -15 cyfmeg./deg. C.

A lbyer of gold was evaporated on both sides of the crystal
to provide better electrical contact, and the high frequency
voltage was supplied to the crystal through the holder shown
in Fig. I. The crystal was held against a brass plate form-
ing one of the electrodes by a light phosphor bronze spring,
which acted as the other electrode. The end of the spring
was divided as shown and contact was made at about the ’
vertical center of the crystal in order to avoid as far as
possible distortion of the sound field due to uneven.mechani-

cal damping of the crystal.

The whole thing was then mounted on a bakelite backing and
clipped to one end of the trough which held the liquid.

The trough is shown in Fig. II. It is simply a brass box
with plate glass sides to avoid optical defects present in
ordinary glass. It is important that the sides of the glass
plates be parallel, as well as the plates themselves in order
that optical effects further than those due to the sound beam
be eliminated. The dimensions of the trough are relatively
unimportant, except that it should be somewhat larger in cross-
section that. the sound beam so that the spreading of the beam
is not affected by the boundaries.

A; the far end of the trough was placed an accustic ab-
sorber, modelled after one described by Fox and Rock(4), and
shown in.Fig. III. It is a brass cylinder with an opening
in the side, around which is built a collector to direct the
sound beam.inside. A brass reflector is placed inside and is
skewed with respect to the opening, so that the sound is re-
flected up and to one side, the energy being dissipated by
multiple reflections within the cylinder. This absorber was
used to minimize the effect of standing waves due to reflec-
tions at the far end of the trough, which would tend to con-
fuse the sound field.

Stirring the liquid should not affect the sound field,
and would remove some of the effects of large temperature
gradients due to high intensities between the sound beam and
the rest of the liquid as well as within the beam itself.

To this end a mechanical stirrer was made, consisting of a

prepellor blade driven by a motor which was rated at 1600 rpm,

This motor was obtained through the courtesy of mr. G. W.
Hoddy of the A. G. Redmond Company, Owosso, Michigan. Hewh
ever, it was found that the flow of liquid was neither rapid
enough nor smooth enough to completely remove all thermally
produced density imhomogeneities, and the result was a blur-
ring of the pattern. In order to avoid this effect and yet
to have better thermal conditions the liquid was stirred
immediately before a photograph was taken, the temperature re-
corded, stirred again after photographing, and the second
temperature recorded.

Temperatures were measured with a thermometer graduated
in tenths of a degree Centigrade, which was found to read
about 0.50 low at the boiling point of water, but was all
right at 00G. The thermometer was placed centrally but not
in the beam.

The optical system.was like that used for an ordinary
grating. The source of light was a high pressure mercury arc,
filtered so as to cut out the blue, most of the red and part
of the yellow. It was found that if the arc was filtered so
as to elimjate all but the green not enough intensity remain-
ed to photograph in any reasonable length of time, The light
was focussed on an adjustable slit by a condensing lens, and
rendered parallel by an achromatic combination. After pass-
ing through the trough and being diffracted, the light was
brought to a focus on the photographic plate by means of a
4800 cm focal length spectacle lens. The optical set-up is
shown diagrammatically in.Fig. IV.

 

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8

The acouiic crystal was driven by a crystal-controlled
power oscillator, whose circuit is shown in.Fig'V. The
oscillator tube was an.RK-20A, a pentode, and was operated
with a d.c. potential of 1000 volts on the plate, fSOOv on
the screen grid, and +45v on the suppressor grid. The feed-
back condenser shown connected between the plate and the
control grid was simply two insulated wires twisted together,
as it was found that any.more capacitance gave too much feed-
back. |

The control crystal was rated at 1806 kcywt0.03%. The
manufacturers recommended that 150 milliamperes by the.maxi-
mum current across the crystal, and to this end a 125 me.
fuse was installed in series with the crystal. .Many helpful
suggestions as to the construction of this oscillator were
obtained from E w Amateur's Handbook (5).

Radio frequency power was transmitted from the oscilla-
tor to the acoustic crystal circuit by means of a link
coupling, also shown in.Fig.‘V. The links at either end con-
sisted of three turns of #lfitinned copper wire, and the trans-
mission line was simply a length of ordinary lamp cord.

This method allows of transmission at loW'potentials, mobility
of the acoustic crystal unit, and still permits relatively
close coupling. The links were mounted inside the two tank
coils in such a manner that they could be turned in order to
vary the coupling if necessary. In this case, as maximum
power'transfer was not particularly desired, no attempt was
made to obtain critical coupling. The maximum.coupling pos-
sible was used at all times, and even then the coupling was

relatively loose.

The acoékic crystal circuit shown in Fig. V reproduced
as exactly as possible the tank circuit of the oscillator, in
order that the impedances be equal. The crystal was then
shunted across the circuit. In both tank coils the coupling
links were mounted on the ground end of the coil, so that the
transmission line was not at a high potential with respect to
the ground.

The power supply for the oscillator consisted of a full-
wave rectifier circuit utilizing two 866 mercury vapor diodes,
as shown in.Fig. VI. The choke-input filter circuit shown is
calculated to give a ripple of approximately 0.75%. The
25,000 ohm bleeder resistance in the power supply serves three
purposes: it supplies a minimum load, allows the filter con-
densers to discharge without arcing when the load is removed,
and also acts as a potential divider to supply the various

voltages for the RKPZOA.

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10

AEXPERIHENTAL PROCEDURE:

With this frequency of 1806 kcy/sec the angle of de-

, viation of the diffraction orders is so small that it was
found necessary to use a very long focal length objective
lens. The lens used was a spectacle lens of focal length
+206 cm, which gave a deviation on the order of 1.6 mm.

The collimating lens was an achromatic combination of focal
length 20 cm, and a very small difference in the position of
this lens made a large difference in the position of the im-
age. To avoid this error the plate holder was set 200 cm
from the objective lens, and the collimator adjusted until
the image was in focus. This could be done as the focal
length of the objective was known rather accurately, and
for a focal length of this magnitude, a slight error in the
setting of the objective affects the position of the colli-
mator very little. Adjustment in this manner appeared to be
the easiest and most accurate way of insuring that the light
incident upon the trough be parallel. Care was taken that
all the components of the Optical system be at the same height,
and perpendicular to the path of the light.

It was shown by BriIlouin that the intensity of the
diffraction orders depends upon the intensity of the sound
wave (see Bergmann, pp. 72-3). This, in turn, depends upon
the power supplied, the distance of the light beam from the
crystal, and upon the liquid in which the sound field is set

up.

11

The closer the light beam is to the acoustic crystal the more
intense are the higher orders, but also the sound field is
somewhat distorted in the immediate neighborhood of the source.
This last is due to the fact that the crystal does not vibrate
exactly like a piston even under good conditions.as well as to
the fact that the effective acoustic aperture is large com-
pared to the distance away. In this work the light beam.passed
through the liquid five centimeters in front of the crystal,
in an attempt to compromise between these two effects.

Eastman Spectroscopic plates V-D were used, and exposure
times were on the order of five minutes in most cases. Some‘
photographs were obtained in times as short as forty seconds,
however. Exposure times were made as short as possible in
order to avoid large temperature differences during the ex-
posure.

The tank circuit of the oscillator was tuned slightly
off the maximum dip in plate current, as at the critical point
the oscillator is.somewhat unstable and the current through
the control crystal is greater.‘ The same procedure was used
in the acoustic crystal circuit, although here the indication
of resonance was a rise in the crystal current. For most of
the measurements the r.f. ammeter indicated about 0.3 amperes,
although it is questionable as to whether this was actually I
the current through the crystal. There was a relatively large
amount of energy radiated from all parts of this circuit - the
tank coil, leads, and even the trough in which the sound was
generated.

The combination radio frequency standard and:mixer-

12

amplifier circuit was used to calibrate a continuous range
oscillator which in turn was used to measure the frequency
of the voltage supplied the acoustic crystal. Signals from
the calibrated oscillator were maxed with those from.the test
oscillator in the combination instrument and tuned to zero
beat. Several measurements made in this manner gave 1806*

4 kcy/sec as the frequency of the acoustic system, No dif-
ference in frequency was detectable when the sound field was
turned on or off.

In order to provide a uniform distribution of charge over
the quartz crystal, used as the source of sound, a coating of
gold was evaporated on each face. 24k gold was obtained from
a dental supply house in the form of small pellets, and only
small amounts were used to give an adequate coating. The
actual evaporating was done in a vacuum system, and strips of
Scotch tape were used to prevent the gold depositing around
the edges and so forming a short circuit when in use.

The distance d in.Eq. (10) were measured on Gaertner
comparator which was graduated to read direct to thousandths
of a millimeter. 'With this particular instrument all readings
had to be taken from.low to high numbers and.the platform.run
in only one direction to eliminate the effect of backlash in
the screw; In.most of the plates the central image was over-
eXposed so the distance between right and left orders was
measured and half this distance taken as the deviation d.

The edge of the orders were in most cases not well defined so
measurements were taken from the centers. To compensate for
random.setting on the centers ten readings were taken for each

of two positions on the plate and the mean of the twenty read-

13

ings used as the value of d. For each liquid two plates were
taken at as nearly the same temperatures as possible in order
to provide a check. In the case of propyl alcohol at a temp
perature below room.temperature only one plate was taken as

it was found that.moisture from.the air condensed on the sides
of the trough and rendered the image too diffuse for photo-
graphing.

The acoustic power input into the trough was.measured as
suggested by Bergmann (p. 37). The liquid, in this case butyl
alcohol, was heated by an electric heater through about the
same temperature range in the same length of time as was caused
by the sound and the electric power measured. This method
assumes that most of the sound energy is converted into heat
in the liquid, which is most probably the case. The index of
refraction of the liquid, the brass sidewall and the air are
all quite different, and it can be shown that the amount of
reflection depends upon the difference in the indices of re-
fraction of the media. However, much of the energy from the
oscillator is lost before it is converted to sound, the electro-
magnetic radiation in the neighborhood of the crystal leads
and the brass trough being sufficient to light a neon test bulb.
Thus although the RK-ZOA tube is rated at 50 watts output,
measurements of the acoustic power indicated only about 7.7
watts. .

Velocity'measurements were made on butyl alcohol, and
vinyl acetate at three different temperatures - one at room
temperature, one below room.temperature, and one several de-

grees above room.temperature. As far as could be determined

14

no measurements had been made on vinyl acetate, and information
as to the temperature dependence of sound velocity in the others
‘was unavaalble. .Measurements were also made on ethyl alcohol

at room temperature.

15

DATA AND RESULTS

Ethyl Alcohol 0235011

Plate No. 1g 13

t °c 25.0 28.5
0. (mm) 1.549 1.562
.fit(am) 0.0705 0.0698
v (m/sec) 1272 1261
dens. (s/cc) 0.7869 0.7865
faad x 10 6 atmfl 79.61 82.55
fat, x 10 5 atmfl 100.68 101.09

r 1626 1323

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19

DISCUSSION qr; RESULTS

Values listed for densities were obtained through the
use of extrapolation formulae given in the International
Critical Tables (6). Values for the isothermal compressibil-
ities were also obtained from this source.

Isothermal compressibilities for butyl alcohol were given
only for 3.05°C and for l7.4°C. These values were interpolated
to 12.00 and 14.100 andI/calculated for these temperatures.

In the absence of more reliable temperature variations relations,
y’was not computed for the other plates. Density and com-
pressibility values for vinyl acetate was not listed, so that

no calculations other than velocities could be made.

_ The adiabatic compressibilities were calculated from.Eq.
(4). This equation shows that the ratio of the specific heats
is also given by the ratio of the isothermal to the adiabatic
compressibility. As the usual way of empressing compressi-
bilities is in terms of reciprocal atmoSpheres, the values
given by Eq. (4):must be multiplied by l,0l3,000 (76 x 13.60 x
980).

There are three measurements of importance in the cal-
culation of velocities: first, the frequency was measured as
described towithin about 0.25%; second, the distance from
the objective lens to the photographic platecould certainly
be measured to within 0.5 cm or 0.25%; third, the distance
d on the platescould be measured to within 0.008 mm.or 0.5%.
This gives an estimated maximum error of one percent.

However, results did not check this closely with those given
in Bergmann (p. 122-3-4-5). Bergmann gives 1254 m/sec for

20

propyl alcohol at 24°C, while interpolation from results
obtained here gives 1223 m/sec, or a difference of about .
0.9%. For butyl alcohol at 23°C, Bergmann gives 1315 m/sec,
as compared to 1272 m/sec obtained here. This a difference
of about 3.3%. One measurement on ethyl alcohol gives 1261
m/sec at 23.5°C, while Bergmann gives 1207 m/sec, for a
difference of 4.5%.

This estimated error will be Just doubled for the
adiabatic compressibilities and the ratio of the specific
heats, for the velocity enters here as the square. For
ethyl alcohol at 23.590 Bergmann gives for)’l.214, and this
determination gives 1.23. Bor butyl alcohol at_23°c Berg- .
mann glistsJ’as 1.160, and these results give 1.35 at 1.4l°0.
For propyl alcohol Bergmann gives 1.162 at 24°C, and this
investigation gives 1.19 at 30.800. Rough interpolation
to 24°C gives 1.23, or about 7% difference.‘

p ad for propyl alcohol at 24°C is givenby Bergnann as
82.9 x 10"6 atm'l, and results here give 84.8 x lo'eatm.’1
or 2.5% difference. /3ad for butyl alcohol at 2390 is given
by Bergmann as 72.5, while these results give 78.0 for a
difference ofoabout 6.2%. For {ethyl alcohol F ad is listed
as 88.3 at 23. 5° C, as compared to 82.55 obtained here,or
a difference of 6,5%. - , , H

An explanation of these differences which are larger

than expected is not readily apparent, there being no obvious

place where the measurements might be at fault.

21
CONCLUSIONS AND GENERAL DISCUSSION

This problem was primarily one of constructing apparatus
and not one of obtaining data. The results obtained from the
data taken, while definitely not of high accuracy, are, how—
ever, good enough to warrant the conclusion that the apparatus
is fundamentally all right, and with further adjustment and
refinement would undoubtedly render rather highly accurate
results.

‘While the apparatus was still in the construction stage,
the first ultrasonic waves produced were detected by the sine
ple expedient of placing a thermometer in front of the acous-
tic crystal. Frictional heat at the liquid-glass and glass-
mercury boundaries due to the passage of the sound waves was
sufficiently great to cause a five to ten degree rise in the
thermometer reading in a very few minutes, while no effect
'was apparent outside the sound beam. This is one more evi-
dence of the rather high concentrations of energy in an
ultrasonic beam.

It was interesting to note that with this particular
apparatus liquids of density greater than one apparently
could not be used. Tuning the acoustic crystal tank circuit
had no effect - the r.f. milliammeter in the acoustic crystal
circuit showed no current, and the whole effect was as if the
crystal circuit were Open. This effect might be eXplained by
the fact that the piezo-electric qualities of a crystal are
reciprocal - not only does the application of a charge to the

faces cause a mechanical deformation, but a mechanical de-

formation causes the appearance of charges on the faces. If

22

the charges are such as to cause an eXpansion, a pressure on
the crystal will cause the appearance of similar charges.

Now let us suppose that the phase of the r.f. current is such
as to cause an eXpansion. At the same time the liquid is ex-
erting a damping force on the crystal, which is probably some
function of the density of the liquid. This would tend to
produce a positive charge on the same face as the current
would be prodching a positive charge, and there would be in
effect an Opposing emf which would be a function of the damp-
ing force and thus a function of the density of the liquid.
This opposing emf could be of such a magnitude as to balance
out the applied emf, thus accounting for the observed re-
sults. This effect showed up in carbon tetrachloride and
glycerine, and also in some liquids whose density was less
than one - for instance, it was well-nigh impossible to set

up a sound field in methyl alcohol, density 0.7921 at 23.800.

(l)

(2)

(5)

(4)

(5)

(6)

(7)

(1)

(2)

(3)

(4)

23

LITERATURE CITED

Bergmann, L., Ultrasonics and Their Scientific and

Industrial AppIIcations I938 John WIIey and
Sons, New York

Richards, W. T. Reviews 2; Nedern Physics,
11, 36, (1939

Debye, P. and F. W. Sears, Proc. Nat. Acad. of
Sci., 18, 409, (Jan. 15, 1932)

Fox, F. E. and G. D. Rock, Phys. Rev.,
541,, 223, (1938)

Radio Amateur's Handbook, 17th Ed., American
Radio Relay League

International Critical Tables, 3 27-35,
McGraw-Hill Book Company, New-York

Suryaprakasam, V., Proc. Indian Acad. Sci. A,
12, 341-9, (1940) As abstracted in Physics
Abstracts 44, 71, (1941)

LITERATURE NOT SPECIFICALLY MENTIONED

Richards, W. T. Jour. of App, Phys.,
2, 298, (1938)

Hubbard, J. 0., Amp Journ of Phys.,
531, 207, (1940)

Peilemeier, W. H. Phys. Rev.,
:33, 1184, (1929)

Fox, F. E. and G. D. Rock, Rev of Sci. Inst.,
.g, 341, (1938)

PHYS)CS-MATH LIE.

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